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Rectangle question

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Fri Jun 30, 2006 5:02 pm    Post subject: Rectangle question Reply with quote

Just a very general question: is there any potential to do anything when just one corner contains only the two deadly candidates? If yes, what should be looked for?

Or are we better off just doing the other usual things until and if a second corner is reduced to the two candidates and the rectangle can now be categorized as Type, 1, 2, etc?
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Fri Jun 30, 2006 7:45 pm    Post subject: Reply with quote

I am not very firm with the uniqueness types.
But when i am stuck, i try to spot potential uniqueness pairs (with maybe having extra candidates in all 4 cells) and then check for strong links for the 2 numbers. If there are any, i look, if starting with one number a deadly pattern is forced. So i found some eliminations, but they did not help much so far.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Fri Jun 30, 2006 8:27 pm    Post subject: UR with one pair Reply with quote

Marty,

First, I agree completely with what ravel says.

The short answer to your question is "yes", but you need to have some strong links. Here is a simple example:

Code:
12  | 123
124 | 125


and suppose this is also an X-wing on <1>. The elimination is: <125> cannot be <2>!

If <125> is <2> it is not <1>, so <124> and <123> are both <1>, which forces the deadly solution since <12> must then be <2>.

I think this kind of pattern is very common, but the reduction is often not very critical.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Fri Jun 30, 2006 8:52 pm    Post subject: Reply with quote

As always, thanks to both of you for the tips.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 01, 2006 7:52 pm    Post subject: An example Reply with quote

Marty,

This puzzle is not only fun to solve, it has an example that illustrates the answer to your question.

Code:
Puzzle: MM063006 Diabolical
+-------+-------+-------+
| . . 1 | 8 . 7 | 3 . . |
| . . . | . 2 . | . 1 6 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| . . 5 | . . . | 8 . . |
| 2 . . | . . . | . . 7 |
| . . 9 | . . . | 1 . . |
+-------+-------+-------+
| . . . | 1 . 2 | 7 . . |
| 8 5 . | . 7 . | . . . |
| . . 6 | 5 . 4 | 9 . . |
+-------+-------+-------+


Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sat Jul 01, 2006 9:56 pm    Post subject: Re: An example Reply with quote

keith wrote:
Marty,

This puzzle is not only fun to solve, it has an example that illustrates the answer to your question.

Code:
Puzzle: MM063006 Diabolical
+-------+-------+-------+
| . . 1 | 8 . 7 | 3 . . |
| . . . | . 2 . | . 1 6 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| . . 5 | . . . | 8 . . |
| 2 . . | . . . | . . 7 |
| . . 9 | . . . | 1 . . |
+-------+-------+-------+
| . . . | 1 . 2 | 7 . . |
| 8 5 . | . 7 . | . . . |
| . . 6 | 5 . 4 | 9 . . |
+-------+-------+-------+


Keith

Keith, is there any chance something is missing? The puzzle is symmetrical except for lack of a given in r3c3. I know you're pretty accurate, but I thought it best to double-check before I start.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sat Jul 01, 2006 10:15 pm    Post subject: Good catch! Reply with quote

Marty,

I did not notice the asymmetry! The original puzzle is here:

http://www.sudoku.org.uk/DailySudoku.asp?day=30/06/2006

and I believe I have posted the same one. The missing symmetrical clue is <4>, I do not believe it changes the path to the solution at all.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sun Jul 02, 2006 3:25 am    Post subject: Reply with quote

I'm not sure whether that asymmetry was deliberate or not, as the few other asymmetrical puzzles I've seen have been VERY asymmetrical, not like this.

At any rate, I did what I could with the basic stuff, plus I found two X-Wings. I did see a 49 rectangle with just one corner containing only the two candidates, but I couldn't do anything with it, even though there was a strong link on the "9."

I couldn't do anything else either, but there was an X-Wing on "9s" that didn't eliminate anything, but I started a chain with them and solved the puzzle that way.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Jul 02, 2006 7:48 am    Post subject: My observations Reply with quote

Marty,

Starting from here:
Code:
+-------------------------+-------------------------+-------------------------+
| 4569    2469    1       | 8       459     7       | 3       2459    2459    |
| 34579   34789   3478    | 49      2       59      | 45      1       6       |
| 4579    24789   2478    | 3       1459    6       | 245     245789  24589   |
+-------------------------+-------------------------+-------------------------+
| 13467   13467   5       | 24679   13469   139     | 8       23469   2349    |
| 2       13468   348     | 469     1345689 13589   | 456     34569   7       |
| 3467    34678   9       | 2467    34568   358     | 1       23456   2345    |
+-------------------------+-------------------------+-------------------------+
| 349     349     34      | 1       3689    2       | 7       34568   3458    |
| 8       5       234     | 69      7       39      | 246     2346    1234    |
| 137     1237    6       | 5       38      4       | 9       238     1238    |
+-------------------------+-------------------------+-------------------------+

the usual stuff gets you to an X-wing on <5>, and then one on <6>, when you are here:
Code:
+-------------------+-------------------+-------------------+
| 6     2     1     | 8     45    7     | 3     459   49    |
| 3     8     7     | 49    2     59    | 45    1     6     |
| 5     9     4     | 3     1     6     | 2     7     8     |
+-------------------+-------------------+-------------------+
| 147   1367  5     | 27    3469  13    | 8     23469 2349  |
| 2     136   8     | 46    34569 135   | 456   34569 7     |
| 47    367   9     | 27    3456  8     | 1     23456 234   |
+-------------------+-------------------+-------------------+
| 9     4     3     | 1     68    2     | 7     68    5     |
| 8     5     2     | 69    7     39    | 46    346   1     |
| 17    17    6     | 5     38    4     | 9     238   23    |
+-------------------+-------------------+-------------------+

After you clear the X-wings, you have
Code:
+-------------------+-------------------+-------------------+
| 6     2     1     | 8     45    7     | 3     459   49    |
| 3     8     7     | 49    2     59    | 45    1     6     |
| 5     9     4     | 3     1     6     | 2     7     8     |
+-------------------+-------------------+-------------------+
| 147   1367  5     | 27    3469  13    | 8     23469 2349  |
| 2     13    8     | 46    349   135   | 456   349   7     |
| 47    367   9     | 27    3456  8     | 1     23456 234   |
+-------------------+-------------------+-------------------+
| 9     4     3     | 1     68    2     | 7     68    5     |
| 8     5     2     | 69    7     39    | 46    34    1     |
| 17    17    6     | 5     38    4     | 9     238   23    |
+-------------------+-------------------+-------------------+

and an XY-wing which says R2C7 is not <4> solves the puzzle.

However, note the Unique Rectangle elimination:

(Edited to fix incorrect elimination.)

R4C2 is not <7>. It forces the deadly solution in R49C12, because of the candidates <47> in R6C1.

As a pencil & paper man, I am finding these reductions (UR + strong links) to be very common but (as in this case) not very essential.

Keith


Last edited by keith on Sun Jul 02, 2006 4:29 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sun Jul 02, 2006 4:03 pm    Post subject: Reply with quote

Keith,

I presumably used the same X-Wings, as mine were also on 5 and 6.

Couple of things I'm not seeing:

1) How a "4" in r6c8 forces a deadly pattern

2) The XY-Wing which eliminates the "4" from r2c7
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Jul 02, 2006 4:36 pm    Post subject: Reply with quote

Marty R. wrote:
Keith,

I presumably used the same X-Wings, as mine were also on 5 and 6.

Couple of things I'm not seeing:

1) How a "4" in r6c8 forces a deadly pattern

2) The XY-Wing which eliminates the "4" from r2c7


Marty,

1) You are correct. I have fixed my original post. (It was late.)

2) The XY-wing is rooted in R8C4; Either R8C7 or R2C4 is <4>.

Sorry about the mistake. I'll just have to find another (correct) example!

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Sun Jul 02, 2006 8:22 pm    Post subject: Reply with quote

Quote:
2) The XY-wing is rooted in R8C4; Either R8C7 or R2C4 is <4>.


They're so much easier to see when the root cells are pointed out. Laughing
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Sun Jul 02, 2006 9:29 pm    Post subject: Reply with quote

Marty R. wrote:

They're so much easier to see when the root cells are pointed out. Laughing

I think they're much harder to spot when they are spread out, and / or in a rectangle.

Anyway, I am finding that Michael Mepham's online diabolical puzzles are much like the DB Saturday puzzles, but perhaps a little easier. Here is today's:

Code:
+----------------------+----------------------+----------------------+
| 148    1248   6      | 12478  5      1248   | 3      124789 1248   |
| 148    12458  124    | 9      127    3      | 28     12478  12468  |
| 7      12348  9      | 1248   6      1248   | 28     1248   5      |
+----------------------+----------------------+----------------------+
| 2      169    5      | 178    179    1689   | 4      89     3      |
| 149    7      14     | 123458 1239   124589 | 2589   6      28     |
| 3      469    8      | 245    29     24569  | 1      259    7      |
+----------------------+----------------------+----------------------+
| 5      128    127    | 123    4      12     | 6      1238   9      |
| 1489   12489  124    | 6      1239   7      | 258    123458 1248   |
| 1469   12469  3      | 125    8      1259   | 7      1245   124    |
+----------------------+----------------------+----------------------+

which can be solved via a couple of X-wings or one (or two) UR's. Choose your poison!.

The Diabolical puzzles are on Friday and Sunday. I have not looked at enough of them to decide if Friday is a different style from Sunday.

http://www.sudoku.org.uk/daily.asp

Best wishes,
Keith
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Mon Jul 03, 2006 2:59 pm    Post subject: A correct example? Reply with quote

Marty,

Try this one:
Code:
Puzzle: DT020306 Diabolical
+-------+-------+-------+
| . 4 . | . 8 . | 5 . . |
| . . . | . 4 3 | 7 6 . |
| . . . | 9 . 1 | . . . |
+-------+-------+-------+
| 2 . 8 | . . 7 | . 9 . |
| . 9 . | . . . | . 1 . |
| . 1 . | 4 . . | 2 . 7 |
+-------+-------+-------+
| . . . | 3 . 9 | . . . |
| . 2 1 | 8 5 . | . . . |
| . . 5 | . 6 . | . 8 . |
+-------+-------+-------+


You get to this stage:

Code:
+----------------+----------------+----------------+
| 37   4    9    | 27   8    6    | 5    23   1    |
| 1    8    2    | 5    4    3    | 7    6    9    |
| 3567 3567 367  | 9    27   1    | 38   4    238  |
+----------------+----------------+----------------+
| 2    35   8    | 16   13   7    | 346  9    3456 |
| 47   9    47   | 26   23   5    | 368  1    368  |
| 356  1    36   | 4    9    8    | 2    35   7    |
+----------------+----------------+----------------+
| 8    67   467  | 3    17   9    | 146  25   25   |
| 369  2    1    | 8    5    4    | 369  7    36   |
| 3479 37   5    | 17   6    2    | 1349 8    34   |
+----------------+----------------+----------------+

There is a UR on <38> in R35C79, which is also an X-wing on <8>. The reduction is R5C9 cannot be <3>.

Not very useful. But, notice the strong links on <3> in C38. One (or both) of R1C8 and R3C3 is <3>. So, R3C7 and R3C9 are not <3>, and that solves the puzzle.

There is another budding UR on <39> in R89C17, which is also an X-wing on <9>. I do not know if it will yield anything.

Best wishes,
Keith
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ravel



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon Jul 03, 2006 4:11 pm    Post subject: Re: A correct example? Reply with quote

keith wrote:

There is another budding UR on <39> in R89C17, which is also an X-wing on <9>. I do not know if it will yield anything.

The 3 in r9c7 could be eliminated, because
r9c7=3 => r8c79<>3 => r8c1=3
But again it does not help.
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Mon Jul 03, 2006 8:24 pm    Post subject: Reply with quote

Keith,

Good puzzles are hard to find. As to the MM that you posted and your comment on them as to how they relate to DB's, they might not be what I'm looking for. But they're certainly an example of the hyperbole ("diabolical") used by puzzle makers.

As to the DT, here is where things came to a halt for me:

Code:
-------------------------------------------------
|37   4    9    |27   8    6    |5    23   1    |
|1    8    2    |5    4    3    |7    6    9    |
|3567 3567 367  |9    27   1    |348  234  248  |
-------------------------------------------------
|2    35   8    |16   13   7    |346  9    3456 |
|47   9    47   |26   23   5    |368  1    368  |
|356  1    36   |4    9    8    |2    35   7    |
-------------------------------------------------
|8    67   46   |3    17   9    |146  245  2456 |
|369  2    1    |8    5    4    |369  7    36   |
|3479 37   5    |17   6    2    |1349 8    34   |
-------------------------------------------------


I didn't get quite as far as you did. Looking at it, I don't know why I eliminated the "7" from r7c3. I also have more candidates in r3c789 and r7c89. The 38 rectangle is no longer there because I eliminated the "3" from r3c9 and have a "4" there instead of the "3." And, of course, I don't have the strong link in c8 which helps solve the puzzle.

I'll look again to see if there's any way I can eliminate more candidates. If not, then I'm sure the puzzle can be solved with forcing chains, assuming I haven't made an error. If I have, I'll just get out the eraser and give it another shot.

Update, 25 minutes later: solved with a chain. It's somewhat disappointing that I couldn't eliminate enough to get to the puzzle-solving strong links.
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keith



Joined: 19 Sep 2005
Posts: 3184
Location: near Detroit, Michigan, USA

PostPosted: Mon Jul 03, 2006 10:30 pm    Post subject: Just a step or two Reply with quote

Marty,

In the position you posted, there is a hidden pair <25> in R7 and B9. Then, R3C8 is <4>, and the strong links are there to take out <3> in R3C7.

I am a pattern maker - you seem to be a member of the chain gang! Rolling Eyes

Keith
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Mon Jul 03, 2006 10:34 pm    Post subject: A hidden pair Reply with quote

Marty R wrote:
It's somewhat disappointing that I couldn't eliminate enough to get to the puzzle-solving strong links.

I sometimes go looking for chains sooner than I ought to. So you're in good (?) company. Smile

There's a hidden pair {2, 5} in row 7 in the position you posted, Marty. That in turn reveals a {2, 3, 5} triplet in column 8, so you can set r3c8 = 4, and then the "strong links" are apparent. dcb

PS I didn't notice the "fork" that Keith was talking about. But I did find a double-implication chain commencing at r6c3 that solved the puzzle -- looking at it with the benefit of hindsight I see that the chain incorporated the "fork." Sometimes the same feature in a puzzle points different ways for different solvers.
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Marty R.



Joined: 12 Feb 2006
Posts: 5178
Location: Rochester, NY, USA

PostPosted: Tue Jul 04, 2006 3:54 am    Post subject: Reply with quote

It looks like both you guys independently found the hidden pair, since based on time of posts, neither of you saw the other's. I'll have to train myself to be alert; I don't recall ever finding a hidden pair or triple, one reason being that I don't know enough to look for them.

Quote:
Looking at it, I don't know why I eliminated the "7" from r7c3.


Just for the record, it was eliminated via a finned X-Wing.

Quote:
That in turn reveals a {2, 3, 5} triplet in column 8, so you can set r3c8 = 4,


This is one of the useless philosophical questions that I think about: why is r3c8 set to "4"? Is it because of eliminations made from the triplet or is it because it was a hidden single? Maybe hidden single shouldn't be a technique because it's always accompanied by a pair, triple, quad, or whatever.

Oh well, I'd be infinitely better off thinking about how to find hidden pairs than this abstract stuff. Rolling Eyes
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